When continents drift apart they usually move so slowly that nobody notices, but since George Bush became president the Atlantic has widened perceptibly.

In the pre-Bush era, disputes between Europe and the US could often be passed off as differences of nuance rather than substance. What is emerging now, however, particularly in relation to the Middle East, is a fundamental difference of approach that will be hard to ignore or resolve.

Let's start, on the eastern side, with Sherard Cowper-Coles, a classics graduate from Oxford, who has spent almost 25 years in the British diplomatic service and is currently Britain's ambassador to Israel.

A couple of weeks ago, largely unnoticed by the media, he gave a lecture at Tel Aviv university entitled "Israel and the Palestinians - a European view".

As befits a classicist, his talk was sprinkled with scholarly references to Thucydides and the devastating Peloponnesian War between ancient Athens and Sparta.

As befits a diplomat, his talk also gushed with expressions of affection for Israel while delivering a few home truths in the delicate manner of someone who broaches the subject of a close friend's body odour.

Without mentioning Israel's increasingly permanent military grip on the Palestinian territories or the massive iron wall now under construction, Mr Cowper-Coles said:

"It must be obvious to every decent Israeli that, whatever short-term measures Israel chooses to take, more than three million Palestinian men, women and children should not be kept for ever confined by military force to a series of security zones in the West Bank and the Gaza Strip."

Turning to the question of Palestinian reform - but ignoring the strident calls from Israel and the US for Yasser Arafat's removal - he supported reform but gave it an unexpected and (for Israel) unwelcome twist:

"In my own personal view, what will be required is nothing less than a large-scale and lasting international presence, led by the United States, overseeing and underpinning first the reform, and then the development, of the Palestinian polity, economy and security apparatus."

"Surely," he continued, "there can be no serious question over the principle of such a benign international intervention, intended to give Palestinians the help with nation-building they deserve, and Israelis the confidence they need to end occupation and settlement."

Israel, of course, has long opposed any idea of international intervention and if the ambassador's remarks did not bring audible gasps from the audience they must at least have caused some shuffling in the seats.

Finally, Mr Cowper-Coles took a swipe at those who spread what he called "the contagion of anxiety and isolation".

"Knowing your enemy is one thing," he told the audience. "Convincing yourself, in elaborately researched detail, that he is an anti-Semite or a terrorist [...] doesn't seem to me to help much.

"In fact, it can be worse than that: the rigorous application of the law of the excluded middle - those not wholly with us are wholly against us - can be deeply destructive of rational discussion. Believe the best of people, and you get some good from them. Believe the worst, and you reap the whirlwind."

These, the ambassador stressed, were personal opinions, not the views of the British government, but in many ways his talk epitomised the European approach to international relations: cajole people along (even if you detest them), highlight the common ground rather than the points of difference, minimise the risks and, if you must rock the boat, rock it gently.

On the opposite side of the Atlantic, none of this goes down well nowadays. It's seen as wimpish, ineffectual and hopelessly old-fashioned.

Like Mr Cowper-Coles, Victor Davis Hanson knows a thing or two about Thucydides - he's Professor of Classics at California State University - but there the similarities stop.

Professor Hanson's area of expertise is ancient warfare, around which he has built a theory of western superiority claiming that certain cultural values - democracy, free markets, the rule of law, etc - bring success on the battlefield.

He expounds these ideas in a book, Carnage and Culture, which has found its way on to college reading lists in the US and is reviewed favourably on Amazon's website by Newt Gingrich, the maverick former Speaker of the House and champion of the new right.

Professor Hanson also has a 60-acre fruit farm in California and writes polemics for the American media, including a regular column in the National Review magazine.

In one recent column, he debunks Edward Said's famous book, Orientalism, as "simplistic" and "superficial". The real problem, he says, is not western misunderstanding of the Arab world but "occidentalism" - which he defines as the Arabs' desire for western products that they either cannot understand or "blindly and in ignorance" loathe.

He backs this up with a series of examples which, presumably, he regards as neither simplistic nor superficial:

"Sheikhs from Saudi Arabia go to London or New York for bypass surgery - not to Cairo or Amman; they buy their Viagra from the States, not from apothecaries in Yemen.

"The Arab street purchases appliances that are made in China or Japan on western blueprints, rather than producing them en masse in Damascus or improving on their designs at Baghdad University."

His latest polemic, in Commentary magazine, takes the form of an attack on Saudi Arabia.

"After the murder of 3,000 Americans, and the various anthrax, dirty-bomb, and suicide-attack scares," he writes, "Americans are finally seeing militant Islam not merely as a different religion, or even as a radical Jim-Jones-like cult, but as a threat to our very existence.

"Saudi Arabia is the placenta of this frightening phenomenon. Its money has financed it; its native terrorists promote it; and its own unhappy citizenry is either amused by or indifferent to its effects upon the world."

While many of Professor Hanson's other complaints about Saudi Arabia - discrimination against women, human rights abuses, corruption - are obvious, the solution that he offers is anything but.

The US, he says, should destabilise the entire Middle East in order to contrive the sort of upheaval that befell the Soviet Union.

"Only by seeking to spark disequilibrium, if not outright chaos, do we stand a chance of ridding the world of the likes of Bin Laden, Arafat, and Saddam Hussein," he says.

"Just as a reconstituted Afghanistan eliminated the satanic Taliban and turned the region's worst regime into a government with real potential, so too a new Iraq might start the fall of dominoes in the Gulf that could wipe away the entire foul nest behind September 11."

It is tempting to dismiss this as the ramblings of a clever but slightly unhinged academic, but Professor Hanson is by no means alone in his views. His remedy for the Middle East is not so much a proposal as a statement of the direction in which US policy appears to be heading.

Iraq is already a declared target and President Bush has indicated, though his speeches, that Iran and Syria are also in his sights. The Israelis, meanwhile, are doing their best to turn the US against Saudi Arabia.

There are several reasons why this is happening. One is that Ariel Sharon, having won approval for his idea that there can be no peace without re-moulding the Palestinians in a form that is more to his liking, has begun to extend it to the rest of the Middle East.

Palestinian terrorism, he argues, is funded and encouraged by Syria, Saudi Arabia, Iran, Iraq and others - so those countries must be changed too.

The second reason is that both Israel and the US persist in their rigorous application of the law of the excluded middle - exactly what the British ambassador warned against.

Those who are not wholly and unreservedly committed to the "war on terrorism" are considered to be siding with terrorists.

Those who disapprove of Ariel Sharon's policies are labelled anti-Israeli or even anti-Semitic.

Worse than that, under the law of the excluded middle positions become more and more polarised, the problems become magnified and require ever more drastic solutions.

The third but perhaps the most important factor is that deliberately creating turmoil throughout the Middle East diverts attention from the underlying problem - the Israeli occupation that has blighted the region for more than half a century and has played a large part in the rise of Islamic militancy.

In the current American climate, it's politically more acceptable to talk of sending a quarter of a million troops to change the regime in Iraq (and to threaten Iran, Syria and Saudi Arabia with similar treatment), than it is to talk of imposing a fair peace for Palestinians.

That, in essence, is where the US and Europe part company. Europeans see the world as it is and seek to deal with its problems; Americans see the world as it would like it to be and seek to change it.

But it's one thing to attempt wholesale change and another to achieve it. As ambassador Cowper-Coles told his Israeli audience: "In the real world, constructive politics is the art of the possible, not the impossible."